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Re: FixedPoint stops "when elements no longer change"?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62875] Re: [mg62776] FixedPoint stops "when elements no longer change"?
*From*: <bsyehuda at gmail.com>
*Date*: Tue, 6 Dec 2005 23:12:10 -0500 (EST)
*References*: <200512050837.DAA08398@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi Steven,
It seems that the answered you got directed you how to represent the results
with desired accuracy but in order to use desired accuracy in FixedPoint[]
you need to set this in the SameTest option. Try the following
FixedPointList[Cos, 1.0, SameTest -> (Abs[#1 - #2] < 0.01 &)]
yehuda
On 12/5/05, Steven T. Hatton <hattons at globalsymmetry.com> wrote:
>
> This is the example in The Mathematica Book for FixedPointList:
>
> FixedPointList[Cos, 1.0]
>
> {1., 0.540302, 0.857553, 0.65429, 0.79348, 0.701369, 0.76396, 0.722102, \
> 0.750418, 0.731404, 0.744237, 0.735605, 0.741425, 0.737507, 0.740147, \
> 0.738369, 0.739567, 0.73876, 0.739304, 0.738938, 0.739184, 0.739018,
> 0.73913, \
> 0.739055, 0.739106, 0.739071, 0.739094, 0.739079, 0.739089, 0.739082, \
> 0.739087, 0.739084, 0.739086, 0.739085, 0.739086, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, \
> 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085, 0.739085}
>
> A bit of poking around showed me that this is using SameQ for SameTest.
>
> "SameQ requires exact correspondence between expressions, except that it
> considers Real numbers equal if their difference is less than the
> uncertainty of either of them."
>
> I guess I'm not seeing all the decimal places used to generate to list
> above. How would I determine the precision used to determine two
> successive values are unchanged?
>
> I tried FixedPointList[N[Cos[#], 2] &, 1.0], but that changed neither the
> display, nor the result.
> --
> The Mathematica Wiki: http://www.mathematica-users.org/
> Math for Comp Sci http://www.ifi.unizh.ch/math/bmwcs/master.html
> Math for the WWW: http://www.w3.org/Math/
>
>
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